How can I make AUCTeX use the spelling dictionary in the same language as babel is loaded with?

This can be done by using language specific hooks in AUCTeX. To automatically load the Danish ispell dictionary when a document includes \usepackage[danish]{babel} put the following in your .emacs:

(add-hook 'TeX-language-dk-hook
      (lambda () (ispell-change-dictionary "danish")))